Answered

Welcome to Westonci.ca, your go-to destination for finding answers to all your questions. Join our expert community today! Experience the ease of finding precise answers to your questions from a knowledgeable community of experts. Explore comprehensive solutions to your questions from a wide range of professionals on our user-friendly platform.

Suppose that [tex]\( A \)[/tex] and [tex]\( B \)[/tex] are sets, defined as follows. Find the intersection and union of [tex]\( A \)[/tex] and [tex]\( B \)[/tex]. Enter the elements of the sets in increasing order, separated by commas. If a set is the empty set, just enter DNE inside the braces given.

[tex]\[
\begin{array}{l}
A = \{2, 3, 6, 7\} \text{ and } B = \{1, 2, 3, 6, 7, 8\} \\
A \cap B = \{\square\} \\
A \cup B = \{\square\}
\end{array}
\][/tex]

Sagot :

GinnyAnswer
Given the sets [tex]\( A = \{2, 3, 6, 7\} \)[/tex] and [tex]\( B = \{1, 2, 3, 6, 7, 8\} \)[/tex], we need to determine the intersection and union of these sets.

### Intersection ([tex]\(A \cap B\)[/tex]):
The intersection of two sets [tex]\( A \)[/tex] and [tex]\( B \)[/tex] is the set of elements that are common to both [tex]\( A \)[/tex] and [tex]\( B \)[/tex].
- Elements in [tex]\( A \)[/tex]: [tex]\( \{2, 3, 6, 7\} \)[/tex]
- Elements in [tex]\( B \)[/tex]: [tex]\( \{1, 2, 3, 6, 7, 8\} \)[/tex]

The common elements are [tex]\( 2, 3, 6, \)[/tex] and [tex]\( 7 \)[/tex].

Thus, the intersection [tex]\(A \cap B = \{2, 3, 6, 7\}\)[/tex].

### Union ([tex]\(A \cup B\)[/tex]):
The union of two sets [tex]\( A \)[/tex] and [tex]\( B \)[/tex] is the set of elements that are in [tex]\( A \)[/tex], in [tex]\( B \)[/tex], or in both.
- Elements in [tex]\( A \)[/tex]: [tex]\( \{2, 3, 6, 7\} \)[/tex]
- Elements in [tex]\( B \)[/tex]: [tex]\( \{1, 2, 3, 6, 7, 8\} \)[/tex]

Combining the elements from both sets (and removing duplicates) gives us: [tex]\( 1, 2, 3, 6, 7, \)[/tex] and [tex]\( 8 \)[/tex].

Thus, the union [tex]\(A \cup B = \{1, 2, 3, 6, 7, 8\}\)[/tex].

### Answer:
[tex]\[ \begin{array}{l} A = \{2, 3, 6, 7\} \\ B = \{1, 2, 3, 6, 7, 8\} \\ A \cap B = \{2, 3, 6, 7\} \\ A \cup B = \{1, 2, 3, 6, 7, 8\} \end{array} \][/tex]
Thank you for visiting our platform. We hope you found the answers you were looking for. Come back anytime you need more information. We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. Thank you for visiting Westonci.ca. Stay informed by coming back for more detailed answers.